| 1 | ||
1.Oblicz całkę bez podstawienia uniwersalnego ∫ | dx | |
| cos2(x)sin(x) |
| dz | dz | ||
−2 | |||
| dx | dy |
| 1 | sin2x+cos2x | |||
∫ | dx= ∫ | dx= | ||
| cos2x*sinx | cos2x*sinx |
| sinx | dx | |||
= ∫ | dx + ∫ | = J1+J2 +C (*) , gdzie | ||
| cos2x | sinx |
| dt | ||
J1= | cosx=t , −sinxdx=dt | = − ∫ | = − ∫t−2dt= | |
| t2 |
| 1 | 1 | |||
= − | = − | ; J2 = | tg12x | i podstaw do (*) | ||
| t | cosx |